3.5.1. Multiple Linear Programming Model

Linear programming is a mathematical method that is used to solve the extremum of a linear objective function under constrained conditions. It provides a scientific basis for the rational utilization of limited resources. In this study, the carbon emission calculation model was added to the multivariate linear programming model to achieve the goal of minimizing carbon emissions. The constraint conditions were set according to the actual situation in the study area. The general linear programming model used was as follows:

$$F(x) = \sum\_{i=1}^{6} k\_i X\_i \tag{8}$$

where *F*(*x*) represents the total carbon emissions; *ki* represents the carbon emission intensity of different land types; and *Xi* represents the decision variable, that is, the acreage of different land types.

With the goal of minimizing carbon emissions from land use in Jinhua by 2030, a multiple linear programming model was built. Cultivated land, woodland, grassland, water area, construction land, and unused land were selected as decision variables *Xi*, and

the carbon emission coefficient from land use in 2018 was selected as *ki*. The planning model developed was as follows:

$$\min = 365.35 \cdot X\_1 - 374 \cdot X\_2 - 21 \cdot X\_3 - 280 \cdot X\_4 + 261853.76 \cdot X\_5 - 5 \cdot X\_6 \tag{9}$$

For the selection of decision variable constraints, we mainly referred to the Fourteenth Five-Year Plan and Long-Range Objectives Through the Year 2035 (hereinafter referred to as the Outline), National Land Planning Outline 2016–2030 (hereinafter referred to as the Plan) with consideration of Jinhua's socio-economic development and status of land-use. The specific constraint conditions are as follows:


According to the analysis above, we set the following constraint conditions for the decision variables set: <sup>6</sup>

$$\sum\_{i=1}^{6} X\_i = 1092199.05, \; X\_i \ge 0 \tag{10}$$

$$(1 - 0.2\%)^{12} \cdot 292914.63 < X\_1 \tag{11}$$

$$(1 - 0.31\%)^{12} \cdot 655048.71 < X\_2 \le (1 + 1.0\%)^{12} \cdot 655048.71 \tag{12}$$

$$\left(1 - 0.45\% \right)^{12} \cdot 21957.48 \le X\_3 \tag{13}$$

$$(1 - 0.02\%)^{12} \cdot 15286.59 \le X\_4 \tag{14}$$

$$(1 + 0.5\%)^{10} \cdot 92522.52 < X\_5 \le \left(1 + 0.93\%\right)^{12} \cdot 92522.52\tag{15}$$

$$(1 - 0.61\%)^{12} \cdot 363.42 \le X\_6 \tag{16}$$
